Geodesic
Explicit Formula for the Spectral Counting Function of the Laplace Operator on a Compact Riemannian Surface of Genus $g>1$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 66-82

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Let the standard Riemannian metric of constant curvature $K=-1$ be given on a compact Riemannian surface of genus $g>1$. Under this condition, for a class of strictly hyperbolic Fuchsian groups, we obtain an explicit expression for the spectral counting function of the Laplace operator in the form of a series over the zeros of the Selberg zeta function.
Keywords: Selberg zeta function, spectral counting function, strictly hyperbolic group. 
@article{FAA_2012_46_2_a6,
     author = {D. A. Popov},
     title = {Explicit {Formula} for the {Spectral} {Counting} {Function} of the {Laplace} {Operator} on a {Compact} {Riemannian} {Surface} of {Genus} $g>1$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {66--82},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a6/}
}
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D. A. Popov. Explicit Formula for the Spectral Counting Function of the Laplace Operator on a Compact Riemannian Surface of Genus $g>1$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 66-82. http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a6/